A model for the mediation of processivity of DNA-targeting proteins by nonspecific binding: dependence on DNA length and presence of obstacles

Facilitated Diffusion Mechanisms in DNA Base Excision Repair and Transcriptional Activation

Preservation of the coding potential of the genome and highly regulated gene expression over the life span of a human are two fundamental requirements of life. These processes require the action of repair enzymes or transcription factors that efficiently recognize specific sites of DNA damage or transcriptional regulation within a restricted time frame of the cell cycle or metabolism. A failure of these systems to act results in accumulated mutations, metabolic dysfunction, and disease. Despite the multifactorial complexity of cellular DNA repair and transcriptional regulation, both processes share a fundamental physical requirement that the proteins must rapidly diffuse to their specific DNA-binding sites that are embedded within the context of a vastly greater number of nonspecific DNA-binding sites. Superimposed on the needle-in-the-haystack problem is the complex nature of the cellular environment, which contains such high concentrations of macromolecules that the time frame for diffusion is expected to be severely extended as compared to dilute solution. Here we critically review the mechanisms for how these proteins solve the needle-in-the-haystack problem and how the effects of cellular macromolecular crowding can enhance facilitated diffusion processes. We restrict the review to human proteins that use stochastic, thermally driven site-recognition mechanisms, and we specifically exclude systems involving energy cofactors or circular DNA clamps. Our scope includes ensemble and single-molecule studies of the past decade or so, with an emphasis on connecting experimental observations to biological function.

Influence of quasi-specific sites on kinetics of target DNA search by a sequence-specific DNA-binding protein

Functions of transcription factors require formation of specific complexes at particular sites in cis-regulatory elements of genes. However, chromosomal DNA contains numerous sites that are similar to the target sequences recognized by transcription factors. The influence of such “quasi-specific” sites on functions of the transcription factors is not well understood at present by experimental means. In this work, using fluorescence methods, we have investigated the influence of quasi-specific DNA sites on the efficiency of target location by the zinc finger DNA-binding domain of the inducible transcription factor Egr-1, which recognizes a 9 bp sequence. By stopped-flow assays, we measured the kinetics of Egr-1’s association with a target site on 143 bp DNA in the presence of various competitor DNAs, including nonspecific and quasi-specific sites. The presence of quasi-specific sites on competitor DNA significantly decelerated the target association by the Egr-1 protein. The impact of the quasi-specific sites depended strongly on their affinity, their concentration, and the degree of their binding to the protein. To quantitatively describe the kinetic impact of the quasi-specific sites, we derived an analytical form of the apparent kinetic rate constant for the target association and used it for fitting to the experimental data. Our kinetic data with calf thymus DNA as a competitor suggested that there are millions of high-affinity quasi-specific sites for Egr-1 among the 3 billion bp of genomic DNA. This study quantitatively demonstrates that naturally abundant quasi-specific sites on DNA can considerably impede the target search processes of sequence-specific DNA-binding proteins.

Searching target sites on DNA by proteins: Role of DNA dynamics under confinement

DNA-binding proteins (DBPs) rapidly search and specifically bind to their target sites on genomic DNA in order to trigger many cellular regulatory processes. It has been suggested that the facilitation of search dynamics is achieved by combining 3D diffusion with one-dimensional sliding and hopping dynamics of interacting proteins. Although, recent studies have advanced the knowledge of molecular determinants that affect one-dimensional search efficiency, the role of DNA molecule is poorly understood. In this study, by using coarse-grained simulations, we propose that dynamics of DNA molecule and its degree of confinement due to cellular crowding concertedly regulate its groove geometry and modulate the inter-communication with DBPs. Under weak confinement, DNA dynamics promotes many short, rotation-decoupled sliding events interspersed by hopping dynamics. While this results in faster 1D diffusion, associated probability of missing targets by jumping over them increases. In contrast, strong confinement favours rotation-coupled sliding to locate targets but lacks structural flexibility to achieve desired specificity. By testing under physiological crowding, our study provides a plausible mechanism on how DNA molecule may help in maintaining an optimal balance between fast hopping and rotation-coupled sliding dynamics, to locate target sites rapidly and form specific complexes precisely.

Balancing between affinity and speed in target DNA search by zinc-finger proteins via modulation of dynamic conformational ensemble

Although engineering of transcription factors and DNA-modifying enzymes has drawn substantial attention for artificial gene regulation and genome editing, most efforts focus on affinity and specificity of the DNA-binding proteins, typically overlooking the kinetic properties of these proteins. However, a simplistic pursuit of high affinity can lead to kinetically deficient proteins that spend too much time at nonspecific sites before reaching their targets on DNA. We demonstrate that structural dynamic knowledge of the DNA-scanning process allows for kinetically and thermodynamically balanced engineering of DNA-binding proteins. Our current study of the zinc-finger protein Egr-1 (also known as Zif268) and its nuclease derivatives reveals kinetic and thermodynamic roles of the dynamic conformational equilibrium between two modes during the DNA-scanning process: one mode suitable for search and the other for recognition. By mutagenesis, we were able to shift this equilibrium, as confirmed by NMR spectroscopy. Using fluorescence and biochemical assays as well as computational simulations, we analyzed how the shifts of the conformational equilibrium influence binding affinity, target search kinetics, and efficiency in displacing other proteins from the target sites. A shift toward the recognition mode caused an increase in affinity for DNA and a decrease in search efficiency. In contrast, a shift toward the search mode caused a decrease in affinity and an increase in search efficiency. This accelerated site-specific DNA cleavage by the zinc-finger nuclease, without enhancing off-target cleavage. Our study shows that appropriate modulation of the dynamic conformational ensemble can greatly improve zinc-finger technology, which has used Egr-1 (Zif268) as a major scaffold for engineering.

Positive and negative impacts of nonspecific sites during target location by a sequence-specific DNA-binding protein: origin of the optimal search at physiological ionic strength

The inducible transcription factor Egr-1, which recognizes a 9-bp target DNA sequence via three zinc-finger domains, rapidly activates particular genes upon cellular stimuli such as neuronal signals and vascular stresses. Here, using the stopped-flow fluorescence method, we measured the target search kinetics of the Egr-1 zinc-finger protein at various ionic strengths between 40 and 400 mM KCl and found the most efficient search at 150 mM KCl. We further investigated the kinetics of intersegment transfer, dissociation, and sliding of this protein on DNA at distinct concentrations of KCl. Our data suggest that Egr-1's kinetic properties are well suited for efficient scanning of chromosomal DNA in vivo. Based on a newly developed theory, we analyzed the origin of the optimal search efficiency at physiological ionic strength. Target association is accelerated by nonspecific binding to nearby sites and subsequent sliding to the target as well as by intersegment transfer. Although these effects are stronger at lower ionic strengths, such conditions also favor trapping of the protein at distant nonspecific sites, decelerating the target association. Our data demonstrate that Egr-1 achieves the optimal search at physiological ionic strength through a compromise between the positive and negative impacts of nonspecific interactions with DNA.

Obstacles may facilitate and direct DNA search by proteins

DNA recognition by DNA-binding proteins (DBPs), which is a pivotal event in most gene regulatory processes, is often preceded by an extensive search for the correct site. A facilitated diffusion process in which a DBP combines three-dimensional diffusion in solution with one-dimensional sliding along DNA has been suggested to explain how proteins can locate their target sites on DNA much faster than predicted by three-dimensional diffusion alone. Although experimental and theoretical studies have recently advanced understanding of the biophysical principles underlying the search mechanism, the process under in vivo cellular conditions is poorly understood. In this study, we used various computational approaches to explore how the presence of obstacle proteins on the DNA influences search efficiency. At a low obstacle occupancy (i.e., when few obstacles occupy sites on the DNA), sliding by the searching DBP may be confined, which may impair search efficiency. The obstacles, however, can be bypassed during hopping events, and the number of bypasses is larger for higher obstacle occupancies. Dynamism on the part of the obstacles may even further facilitate search kinetics. Our study shows that the nature and efficiency of the search process may be governed not only by the intrinsic properties of the DBP and the salt concentration of the medium, but also by the in vivo association of DNA with other macromolecular obstacles, their location, and occupancy.

Stopped-flow fluorescence kinetic study of protein sliding and intersegment transfer in the target DNA search process

Kinetic characterizations of protein translocation on DNA are nontrivial because the simultaneous presence of multiple different mechanisms makes it difficult to extract the information specific to a particular translocation mechanism. In this study, we have developed new approaches for the kinetic investigations of proteins' sliding and intersegment transfer (also known as "direct transfer") in the target DNA search process. Based on the analytical expression of the mean search time for the discrete-state stochastic model, we derived analytical forms of the apparent rate constant kapp for protein-target association in systems involving competitor DNA and the intersegment transfer mechanism. Our analytical forms of kapp facilitate the experimental determination of the kinetic rate constants for intersegment transfer and sliding in the target association process. Using stopped-flow fluorescence data for the target association kinetics along with the analytical forms of kapp, we have studied the translocation of the Egr-1 zinc-finger protein in the target DNA association process. Sliding was analyzed using the DNA-length-dependent kapp data. Using the dependence of kapp on the concentration of competitor DNA, we determined the second-order rate constant for intersegment transfer. Our results indicate that a major pathway in the target association process for the Egr-1 zinc-finger protein is the one involving intersegment transfer to a nonspecific site and the subsequent sliding to the target.

A quantitative model of ERK MAP kinase phosphorylation in crowded media

Cytoplasm contains a large number of macromolecules at extremely high densities. How this striking nature of intracellular milieu called macromolecular crowding affects intracellular signaling remains uncharacterized. Here, we examined the effect of macromolecular crowding on ERK MAPK phosphorylation by MEK MAPKK. Addition of polyethylene glycol-6000 (PEG-6000) as a crowder to mimic intracellular environments, elicited a biphasic response to the overall ERK phosphorylation rate. Furthermore, probability of processive phosphorylation (processivity) of tyrosine and threonine residues within the activation loop on ERK increased non-linearly for increasing PEG-6000 concentration. Based on the experimental data, we developed for the first time a mathematical model integrating all of the effects of thermodynamic activity, viscosity, and processivity in crowded media, and found that ERK phosphorylation is transition-state-limited reaction. The mathematical model allows accurate estimation of the effects of macromolecular crowding on a wide range of reaction kinetics, from transition-state-limited to diffusion-limited reactions.

How do proteins locate specific targets in DNA?

Many aspects of biology depend on the ability of DNA-binding proteins to locate specific binding sites within the genome. Interest in this target search problem has been reinvigorated through the recent development of microscopy-based technologies capable of tracking individual proteins in real-time as they search for binding sites. In this review we discuss how two different proteins, lac repressor and RNA polymerase, have solved the target search problem through seemingly different mechanisms, with an emphasis on how recent in vitro single-molecule studies have influenced our understanding of these reactions.

BDflex: a method for efficient treatment of molecular flexibility in calculating protein-ligand binding rate constants from brownian dynamics simulations

A method developed by Northrup et al. [J. Chem. Phys. 80, 1517 (1984)] for calculating protein-ligand binding rate constants (k(a)) from brownian dynamics (BD) simulations has been widely used for rigid molecules. Application to flexible molecules is limited by the formidable computational cost to treat conformational fluctuations during the long BD simulations necessary for k(a) calculation. Here, we propose a new method called BDflex for k(a) calculation that circumvents this problem. The basic idea is to separate the whole space into an outer region and an inner region, and formulate k(a) as the product of k(E) and η(d), which are obtained by separately solving exterior and interior problems. k(E) is the diffusion-controlled rate constant for the ligand in the outer region to reach the dividing surface between the outer and inner regions; in this exterior problem conformational fluctuations can be neglected. η(d) is the probability that the ligand, starting from the dividing surface, will react at the binding site rather than escape to infinity. The crucial step in reducing the determination of η(d) to a problem confined to the inner region is a radiation boundary condition imposed on the dividing surface; the reactivity on this boundary is proportional to k(E). By confining the ligand to the inner region and imposing the radiation boundary condition, we avoid multiple-crossing of the dividing surface before reaction at the binding site and hence dramatically cut down the total simulation time, making the treatment of conformational fluctuations affordable. BDflex is expected to have wide applications in problems where conformational fluctuations of the molecules are crucial for productive ligand binding, such as in cases where transient widening of a bottleneck allows the ligand to access the binding pocket, or the binding site is properly formed only after ligand entrance induces the closure of a lid.

Computational models for large-scale simulations of facilitated diffusion

The binding of site-specific transcription factors to their genomic target sites is a key step in gene regulation. While the genome is huge, transcription factors belong to the least abundant protein classes in the cell. It is therefore fascinating how short the time frame is that they require to home in on their target sites. The underlying search mechanism is called facilitated diffusion and assumes a combination of three-dimensional diffusion in the space around the DNA combined with one-dimensional random walk on it. In this review, we present the current understanding of the facilitated diffusion mechanism and identify questions that lack a clear or detailed answer. One way to investigate these questions is through stochastic simulation and, in this manuscript, we support the idea that such simulations are able to address them. Finally, we review which biological parameters need to be included in such computational models in order to obtain a detailed representation of the actual process.

Classes of fast and specific search mechanisms for proteins on DNA

Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.

First-passage time analysis of a one-dimensional diffusion-reaction model: application to protein transport along DNA

BACKGROUND

Proteins search along the DNA for targets, such as transcription initiation sequences, according to one-dimensional diffusion, which is interrupted by micro- and macro-hopping events and intersegmental transfers that occur under close packing conditions.

RESULTS

A one-dimensional diffusion-reaction model in the form of difference-differential equations is proposed to analyze the nonequilibrium protein sliding kinetics along a segment of bacterial DNA. A renormalization approach is used to derive an expression for the mean first-passage time to arrive at sites downstream of the origin from the occupation probabilities given by the individual transport equations. Monte Carlo simulations are employed to assess the validity of the proposed approach, and all results are interpreted within the context of bacterial transcription.

CONCLUSIONS

Mean first-passage times decrease with increasing reaction rates, indicating that, on average, surviving proteins more rapidly locate downstream targets than their reaction-free counterparts, but at the price of increasing rarity. Two qualitatively different screening regimes are identified according to whether the search process operates under "small" or "large" values for the dissociation rate of the protein-DNA complex. Lower bounds are placed on the overall search time for varying reactive conditions. Good agreement with experimental estimates requires the reaction rate reside near the transition between both screening regimes, suggesting that biology balances a need for rapid searches against maximum exploration during each round of the sliding phase.

Rapid search for specific sites on DNA through conformational switch of nonspecifically bound proteins

We develop a theory for the rapid search of specific sites on DNA, via a mechanism in which a nonspecifically-bound protein can switch between two conformations. In the "inactive" conformation, the bound protein has favorable, nonspecific interactions with the DNA, but cannot be recognized by the target site. In the "active" conformation, the protein is recognized by the target site but has a very rugged energy surface elsewhere on the DNA. The rate constant for protein binding to the specific site is calculated by an approach in which the protein, after reaching the DNA surface via 3D diffusion, searches for the target site via 1D diffusion while being allowed to escape to the bulk solution. Mindful of the pitfalls of many previous approximate treatments, we validate our approach against a rigorous solution of the problem when the protein has a fixed conformation. In the 1D diffusion toward the specific site, a conformationally switchable protein predominantly adopts the inactive conformation due to the favorable nonspecific interactions with the DNA, thus maximizing the 1D diffusion constant and minimizing the chance of escape to the bulk solution. Once at the target site, a transition to the active conformation allows the protein to be captured. This induced-switch mechanism provides robust speedup of protein-DNA binding rates, and appears to be adopted by many transcription factors and DNA-modifying enzymes.

The diffusion constant of a labeled protein sliding along DNA

Long ago inferred by biochemists, the linear diffusion of proteins along DNA has recently been observed at a single-molecule level using fluorescence microscopy. This imaging technique requires labeling the protein of interest with a fluorophore, usually an organic nanosized dye that is not supposed to impact the dynamics of the protein. Yet individual proteins can also be tracked using much larger labels, like quantum dots or beads. We investigate here the impact of such a large label on the protein diffusion along DNA. Solving a Fokker-Planck equation, we estimate the diffusion constant of a protein-label complex diffusing in a periodic potential that mimics the DNA-protein interaction, the link between the protein and the label being modeled as a Hookean spring. Our results indicate that the diffusion constant can generally be calculated by considering that the motion of the protein in the DNA potential is decoupled from the Brownian motion of the label. Our conclusions are in good agreement with the experimental results we obtained with the restriction enzyme EcoRV, assuming a rotation-coupled diffusion of the enzyme along DNA.

Physics of protein-DNA interactions: mechanisms of facilitated target search

One of the most critical aspects of protein-DNA interactions is the ability of protein molecules to quickly find and recognize specific target sequences on DNA. Experimental measurements indicate that the corresponding association rates to few specific sites among large number of non-specific sites are typically large. For some proteins they might be even larger than maximal allowed three-dimensional diffusion rates. Although significant progress in understanding protein search and recognition of targets on DNA has been achieved, detailed mechanisms of these processes are still strongly debated. Here we present a critical review of current theoretical approaches and some experimental observations in this area. Specifically, the role of lowering dimensionality, non-specific interactions, diffusion along the DNA molecules, protein and target sites concentrations, and electrostatic effects are critically analyzed. Possible future directions and outstanding problems are also presented and discussed.

Dynamic strategies for target-site search by DNA-binding proteins

Gene regulatory proteins find their target sites on DNA remarkably quickly; the experimental binding rate for lac repressor is orders-of-magnitude higher than predicted by free diffusion alone. It has been proposed that nonspecific binding aids the search by allowing proteins to slide and hop along DNA. We develop a reaction-diffusion theory of protein translocation that accounts for transport both on and off the strand and incorporates the physical conformation of DNA. For linear DNA modeled as a wormlike chain, the distribution of hops available to a protein exhibits long, power-law tails that make the long-time displacement along the strand superdiffusive. Our analysis predicts effective superdiffusion coefficients for given nonspecific binding and unbinding rate parameters. Translocation rate exhibits a maximum at intermediate values of the binding rate constant, while search efficiency is optimized at larger binding rate constant values. Thus, our theory predicts a region of values of the nonspecific binding and unbinding rate parameters that balance the protein translocation rate and the efficiency of the search. Published data for several proteins falls within this predicted region of parameter values.

Rate theories for biologists

Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.

Facilitated search of proteins on DNA: correlations are important

A starting point of many biological processes is protein binding to specific regions on DNA. Although typical concentrations of DNA-binding proteins are low, and target sites are typically buried among huge number of non-specific sites, the search process is frequently achieved at a remarkably fast rate. For some proteins it has been confirmed that association rates might be even larger than the maximal allowed three-dimensional diffusion rates. The current theoretical view of this phenomenon is based on the idea of lowering dimensionality, i.e., the overall search process is viewed as a combination of uncorrelated three-dimensional excursions in the solution and one-dimensional hoppings on DNA. However, some predictions of this theoretical picture contradict recent single-molecule measurements of protein diffusion processes. An alternative theoretical approach points out the importance of correlations during the search process that appear due to non-specific interactions between protein and DNA molecules. To test different theoretical ideas we performed extensive lattice Monte Carlo computer simulations of the facilitated diffusion. Our results revealed that correlations are important, and the acceleration in the search could only be achieved at some intermediate non-specific binding energies and protein concentrations. Physico-chemical aspects and the origins of these correlations are discussed.

Packaging effects on site-specific DNA-protein interactions

We show that the rate of site-specific association of a protein molecule of interest with the DNA chain can be approximately 10(2) times higher than that of the three-dimensional diffusion-controlled collision rate limit approximately 10(8) mol(-1) s(-1) only when the protein molecule of interest searches for its specific site on the DNA chain in a reduced dimensional space with a dimensionality dr of dr<1. Upon considering the concurrent dynamics of the linear DNA chain that is embedded in a d-dimensional space along with the one-dimensional diffusion dynamics of the nonspecifically bound protein molecule on the DNA chain, we derive the generalized scaling law epsilon approximately 2(3(2-d)+3), where epsilon is the number of times by which the rate of site-specific association of the protein molecule with the DNA chain can be enhanced over the three-dimensional diffusion-controlled collision rate limit and d is the dimensionality of the reduced search space. Using the analogy between the self-intersection loop length in the theory of random walks and the ring-closure events in the theory of site specific interactions of a protein molecule with the DNA chain, we further show that the extent of packaging and volume compression of the genomic DNA inside the living cell is designed in such a way that the efficiency of the protein molecule in the process of searching for its specific site on the genomic DNA is a maximum. Our simulation results suggest that the volume compression factor theta which is the ratio between the total volume of the living cell and the volume occupied by the DNA chain along with all the other bound protein molecules should be such that theta>or=100 for an efficient site specific interaction of a protein molecule of interest with the linear DNA chain that is embedded in a three-dimensional space. Our theoretical and simulation results agree well with the E. coli cellular system.

Facilitated diffusion with DNA coiling

When DNA-binding proteins search for their specific binding site on a DNA molecule they alternate between linear 1-dimensional diffusion along the DNA molecule, mediated by nonspecific binding, and 3-dimensional volume excursion events between successive dissociation from and rebinding to DNA. If the DNA molecule is kept in a straight configuration, for instance, by optical tweezers, these 3-dimensional excursions may be divided into long volume excursions and short hops along the DNA. These short hops correspond to immediate rebindings after dissociation such that a rebinding event to the DNA occurs at a site that is close to the site of the preceding dissociation. When the DNA molecule is allowed to coil up, immediate rebinding may also lead to so-called intersegmental jumps, i.e., immediate rebindings to a DNA segment that is far away from the unbinding site when measured in the chemical distance along the DNA, but close by in the embedding 3-dimensional space. This effect is made possible by DNA looping. The significance of intersegmental jumps was recently demonstrated in a single DNA optical tweezers setup. Here we present a theoretical approach in which we explicitly take the effect of DNA coiling into account. By including the spatial correlations of the short hops we demonstrate how the facilitated diffusion model can be extended to account for intersegmental jumping at varying DNA densities. It is also shown that our approach provides a quantitative interpretation of the experimentally measured enhancement of the target location by DNA-binding proteins.

The effects of intersegmental transfers on target location by proteins

We study a model of protein searching for a target, using facilitated diffusion, on a DNA molecule confined in a finite volume. The model includes three distinct pathways for facilitated diffusion: (a) sliding--in which the protein diffuses along the contour of the DNA, (b) jumping--where the protein travels between two sites along the DNA by three-dimensional diffusion and finally (c) intersegmental transfer--which allows the protein to move from one site to another by transiently binding both at the same time. The typical search time is calculated using scaling arguments which are verified numerically. Our results suggest that the inclusion of intersegmental transfer (i) decreases the search time considerably, (ii) makes the search time much more robust to variations in the parameters of the model and (iii) that the optimal search time occurs in a regime very different than that found for models which ignore intersegmental transfers. The behavior we find is rich and shows surprising dependences, for example on the DNA length.

How DNA coiling enhances target localization by proteins

Many genetic processes depend on proteins interacting with specific sequences on DNA. Despite the large excess of nonspecific DNA in the cell, proteins can locate their targets rapidly. After initial nonspecific binding, they are believed to find the target site by 1D diffusion ("sliding") interspersed by 3D dissociation/reassociation, a process usually referred to as facilitated diffusion. The 3D events combine short intrasegmental "hops" along the DNA contour, intersegmental "jumps" between nearby DNA segments, and longer volume "excursions." The impact of DNA conformation on the search pathway is, however, still unknown. Here, we show direct evidence that DNA coiling influences the specific association rate of EcoRV restriction enzymes. Using optical tweezers together with a fast buffer exchange system, we obtained association times of EcoRV on single DNA molecules as a function of DNA extension, separating intersegmental jumping from other search pathways. Depending on salt concentration, targeting rates almost double when the DNA conformation is changed from fully extended to a coiled configuration. Quantitative analysis by an extended facilitated diffusion model reveals that only a fraction of enzymes are ready to bind to DNA. Generalizing our results to the crowded environment of the cell we predict a major impact of intersegmental jumps on target localization speed on DNA.

Generalized theory of site-specific DNA-protein interactions

We develop a generalized theory of the site-specific DNA-protein interactions, which includes both the static as well as the dynamical factors influencing the one-dimensional diffusion of the nonspecifically bound protein molecule which is in the process of searching for the specific site on the DNA lattice. We argue that the chemically driven condensation of the DNA molecule introduces a static distribution in the one-dimensional phenomenological diffusion coefficient associated with the protein molecule and the conformational dynamics of the DNA introduces temporal fluctuations in the one-dimensional diffusion coefficient over the static distribution. We further derive the generalized inequality conditions and the scaling laws which are required to enhance the three-dimensional diffusion controlled site-specific association rate to an arbitrary order. Our model predicts that when the degree of condensation of the DNA molecule under consideration is very high, then the probability distribution associated with the stationary state one-dimensional diffusion coefficient variable as well as the stationary state one-dimensional diffusion length variable will be a flat one. Further analysis reveals that to achieve a site-specific association rate which is higher than that of the three-dimensional diffusion controlled rate, the one-dimensional diffusion length associated with the dynamics of the nonspecifically bound protein molecule on the DNA lattice should fall in certain critical ranges. Comparison of our theoretical results with the recent experimental observations reveals that when the DNA molecule is under a stretched condition, then the static distribution of the one-dimensional diffusion coefficient associated with the dynamics of the protein molecule on the DNA lattice is a Gaussian and therefore the fluctuations in the one-dimensional diffusion coefficient generated by the dynamical factors are confined in a harmonic type potential.

Domains in the XPA protein important in its role as a processivity factor

XPA is a protein essential for nucleotide excision repair (NER) where it is thought to function in damage recognition/verification. We have proposed an additional role, that of a processivity factor, conferring a processive mechanism of action on XPF and XPG, the endonucleases, involved in NER. The present study was undertaken to examine the domain(s) in the XPA gene that are important for the ability of the XPA protein to function as a processivity factor. Using site-directed mutagenesis, mutations were created in several of the exons of XPA and mutant XPA proteins produced. The results showed that the DNA binding domain of XPA is critical for its ability to act as a processivity factor. Mutations in both the zinc finger motif and the large basic cleft in this domain eliminated the ability of XPA to confer a processive mechanism of action on the endonucleases involved in NER.

A quantitative study of lambda-phage SWITCH and its components

We propose what we believe is a new model to quantitatively describe the lambda-phage SWITCH system. The model incorporates facilitated transfer mechanism of transcription factor, which can be simplified into a two-step reaction. We first sequentially obtain two indispensable parameters by fitting our model to experimental data of two simple systems, and then apply them to study the natural lambda-SWITCH system. By incorporating the facilitated transfer mechanism, we find that in RecA(-) host Escherichia coli, the wild-type lambda-lysogenic state is in a monostable regime rather than in a bistable regime. Furthermore, the model explains the weak role of Cro protein and probably sheds light on the evolution of lambda-Cro protein, which is known to be structurally distinct from the other Cros in lambdoid family members.

Strong physical constraints on sequence-specific target location by proteins on DNA molecules

Sequence-specific binding to DNA in the presence of competing non-sequence-specific ligands is a problem faced by proteins in all organisms. It is akin to the problem of parking a truck at a loading bay by the side of a road in the presence of cars parked at random along the road. Cars even partially covering the loading bay prevent correct parking of the truck. Similarly on DNA, non-specific ligands interfere with the binding and function of sequence-specific proteins. We derive a formula for the probability that the loading bay is free from parked cars. The probability depends on the size of the loading bay and allows an estimation of the size of the footprint on the DNA of the sequence-specific protein by assaying protein binding or function in the presence of increasing concentrations of non-specific ligand. Assaying for function gives an 'activity footprint'; the minimum length of DNA required for function rather than the more commonly measured physical footprint. Assaying the complex type I restriction enzyme, EcoKI, gives an activity footprint of approximately 66 bp for ATP hydrolysis and 300 bp for the DNA cleavage function which is intimately linked with translocation of DNA by EcoKI. Furthermore, considering the coverage of chromosomal DNA by proteins in vivo, our theory shows that the search for a specific DNA sequence is very difficult; most sites are obscured by parked cars. This effectively rules out any significant role in target location for mechanisms invoking one-dimensional, linear diffusion along DNA.

APOBEC3G DNA deaminase acts processively 3' --> 5' on single-stranded DNA

Akin to a 'Trojan horse,' APOBEC3G DNA deaminase is encapsulated by the HIV virion. APOBEC3G facilitates restriction of HIV-1 infection in T cells by deaminating cytosines in nascent minus-strand complementary DNA. Here, we investigate the biochemical basis for C --> U targeting. We observe that APOBEC3G binds randomly to single-stranded DNA, then jumps and slides processively to deaminate target motifs. When confronting partially double-stranded DNA, to which APOBEC3G cannot bind, sliding is lost but jumping is retained. APOBEC3G shows catalytic orientational specificity such that deamination occurs predominantly 3' --> 5' without requiring hydrolysis of a nucleotide cofactor. Our data suggest that the G --> A mutational gradient generated in viral genomic DNA in vivo could result from an intrinsic processive directional attack by APOBEC3G on single-stranded cDNA.

Measurement of the contributions of 1D and 3D pathways to the translocation of a protein along DNA

Proteins that act at specific DNA sequences bind DNA randomly and then translocate to the target site. The translocation is often ascribed to the protein sliding along the DNA while maintaining continuous contact with it. Proteins also can move on DNA by multiple cycles of dissociation/reassociation within the same chain. To distinguish these pathways, a strategy was developed to analyze protein motion between DNA sites. The strategy reveals whether the protein maintains contact with the DNA as it transfers from one site to another by sliding or whether it loses contact by a dissociation/reassociation step. In reactions at low salt, the test protein stayed on the DNA as it traveled between sites, but only when the sites were <50 bp apart. Transfers of >30 bp at in vivo salt, and over distances of >50 bp at any salt, always included at least one dissociation step. Hence, for this enzyme, 1D sliding operates only over short distances at low salt, and 3D dissociation/reassociation is its main mode of translocation.

How do biomolecular systems speed up and regulate rates?

The viability of a biological system depends upon careful regulation of the rates of various processes. These rates have limits imposed by intrinsic chemical or physical steps (e.g., diffusion). These limits can be expanded by interactions and dynamics of the biomolecules. For example, (a) a chemical reaction is catalyzed when its transition state is preferentially bound to an enzyme; (b) the folding of a protein molecule is speeded up by specific interactions within the transition-state ensemble and may be assisted by molecular chaperones; (c) the rate of specific binding of a protein molecule to a cellular target can be enhanced by mechanisms such as long-range electrostatic interactions, nonspecific binding and folding upon binding; (d) directional movement of motor proteins is generated by capturing favorable Brownian motion through intermolecular binding energy; and (e) conduction and selectivity of ions through membrane channels are controlled by interactions and the dynamics of channel proteins. Simple physical models are presented here to illustrate these processes and provide a unifying framework for understanding speed attainment and regulation in biomolecular systems.